6x - 5y= 20 and 5y - 6x= -20

Is there a solution, infinity, A point

Consistent or inconsistent

dependent or independent

To determine if the given system of equations has a solution and whether that solution is unique or infinite, we need to examine the consistency and dependence of the equations.

First, let's rearrange the second equation to match the format of the first equation:
5y - 6x = -20
Rearranging, we have:
6x - 5y = 20

We can observe that the two equations are identical, just with the coefficients in a different order. This implies that the system is consistent and the equations are dependent. In other words, the two lines represented by these equations are coincident (they lie on top of each other) and have infinite solutions.

Visually, if you were to graph these equations, you would see that they represent the same line, intersecting at all points along that line. Therefore, the solution to the system is all points along the line represented by these equations.

In conclusion, the system of equations has an infinite number of solutions.